arXiv subjects

Tobias Dietz

Publications and source records attributed to Tobias Dietz.

6 recordsLinked to original sources

arXiv2025

A Study in Dataset Distillation for Image Super-Resolution

Dataset distillation aims to compress large datasets into compact yet highly informative subsets that preserve the training behavior of the original data. While this concept has gained traction in classification, its potential for image Super-Resolution (SR) remains largely untapped. In this work, we conduct the first systematic study of dataset distillation for SR, evaluating both pixel- and latent-space formulations. We show that a distilled dataset, occupying only 8.88% of the original size, can train SR models that retain nearly the same reconstruction fidelity as those trained on full datasets. Furthermore, we analyze how initialization strategies and distillation objectives affect efficiency, convergence, and visual quality. Our findings highlight the feasibility of SR dataset distillation and establish foundational insights for memory- and compute-efficient generative restoration models.

cs.CV↗

arXiv2020

Sparsifying Parity-Check Matrices

Parity check matrices (PCMs) are used to define linear error correcting codes and ensure reliable information transmission over noisy channels. The set of codewords of such a code is the null space of this binary matrix. We consider the problem of minimizing the number of one-entries in parity-check matrices. In the maximum-likelihood (ML) decoding method, the number of ones in PCMs is directly related to the time required to decode messages. We propose a simple matrix row manipulation heuristic which alters the PCM, but not the code itself. We apply simulated annealing and greedy local searches to obtain PCMs with a small number of one entries quickly, i.e. in a couple of minutes or hours when using mainstream hardware. The resulting matrices provide faster ML decoding procedures, especially for large codes.

cs.IT↗

arXiv2020

The {0,1}-knapsack problem with qualitative levels

A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this relation defines a preorder. We propose a dynamic programming algorithm to compute the entire set of non-dominated rank cardinality vectors and we state two greedy algorithms, which efficiently compute a single efficient solution.

cs.DS↗

arXiv2019

A Reduced-Complexity Projection Algorithm for ADMM-based LP Decoding

The Alternating Direction Method of Multipliers has recently been adapted for Linear Programming Decoding of Low-Density Parity-Check codes. The computation of the projection onto the parity polytope is the core of this algorithm and usually involves a sorting operation, which is the main effort of the projection. In this paper, we present an algorithm with low complexity to compute this projection. The algorithm relies on new findings in the recursive structure of the parity polytope and iteratively fixes selected components. It requires up to 37% less arithmetical operations compared to state-of-the-art projections. Additionally, it does not involve a sorting operation, which is needed in all exact state-of-the-art projection algorithms. These two benefits make it appealing for efficient hard- and software implementations.

cs.IT↗

arXiv2018

Introducing Multiobjective Complex Systems

This article focuses on the optimization of a complex system which is composed of several subsystems. On the one hand, these subsystems are subject to multiple objectives, local constraints as well as local variables, and they are associated with an own, subsystem-dependent decision maker. On the other hand, these subsystems are interconnected to each other by global variables or linking constraints. Due to these interdependencies, it is in general not possible to simply optimize each subsystem individually to improve the performance of the overall system. This article introduces a formal graph-based representation of such complex systems and generalizes the classical notions of feasibility and optimality to match this complex situation. Moreover, several algorithmic approaches are suggested and analyzed.

math.OC↗

arXiv2018

Shortest Paths with Ordinal Weights

We investigate the single-source-single-destination "shortest" paths problem in acyclic graphs with ordinal weighted arc costs. We define the concepts of ordinal dominance and efficiency for paths and their associated ordinal levels, respectively. Further, we show that the number of ordinally non-dominated paths vectors from the source node to every other node in the graph is polynomially bounded and we propose a polynomial time labeling algorithm for solving the problem of finding the set of ordinally non-dominated paths vectors from source to sink.

cs.DS↗